{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "3ea03585",
   "metadata": {},
   "source": [
    "# 基本原理\n",
    "## 模型介绍\n",
    "knn是一种监督式学习方法<br>\n",
    "其工作机制十分简单：给定测试样本，基于某种距离度量找出训练集中与其最靠近的k个样本，然后基于这k个临近点的信息来进行该测试样本所属类别的预测。<br>\n",
    "通常而言，在分类任务中一般使用“投票法”，即选择k个样本中出现最多的类别标记作为输出结果；<br>\n",
    "在回归任务中一般使用“平均法”，即将这k个样本的实际值的平均值作为输出结果\n",
    "## 模型分析\n",
    "作为一种监督式学习模型，knn不存在显式的模型训练过程<br>\n",
    "也就是说，在训练阶段我们只需要把样本保存起来，训练时间开销几乎为0<br>\n",
    "在机器学习中，这种模式又被称为\"懒惰学习\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf08c4e",
   "metadata": {},
   "source": [
    "# python代码实现\n",
    "python sklearn neighbors包下包含了全部knn及其拓展算法的实现<br>\n",
    "KNeighborsClassifier中比较重要的超参数有：\n",
    "1. n_neighbors 表示k值\n",
    "2. weights \"uniform\"|\"distance\" 表示进行投票时每个数据点的权值\n",
    "3. metric \"minkowski\"\n",
    "4. p 2 二者共同定义距离计算公式式欧氏距离，即闵氏距离p=2的情况"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b0e8dc70",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import warnings \n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "iris_x, iris_y = load_iris(return_X_y=True)\n",
    "# 为了可视化方便，我们只取iris中的前两个属性\n",
    "iris_x = iris_x[:,:2]\n",
    "x_train, x_test, y_train, y_test \\\n",
    "    = train_test_split(iris_x,iris_y,test_size=0.2,random_state=42)\n",
    "knn_clf = KNeighborsClassifier(n_neighbors=7)\n",
    "knn_clf.fit(x_train,y_train)\n",
    "y_pred = knn_clf.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3c90a7b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.0, 8.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "mpl.rcParams[\"font.sans-serif\"] = \"SimHei\"\n",
    "fig,ax = plt.subplots(1,3,figsize=(12,4),\n",
    "                     facecolor=\"whitesmoke\",edgecolor=\"gray\")\n",
    "class0 = []\n",
    "class1 = []\n",
    "class2 = []\n",
    "for idx,cls in enumerate(iris_y):\n",
    "    if cls == 0:\n",
    "        class0.append(iris_x[idx,:])\n",
    "    elif cls == 1:\n",
    "        class1.append(iris_x[idx,:])\n",
    "    else:\n",
    "        class2.append(iris_x[idx,:])\n",
    "ax[0].set_title(\"original dataset class\")\n",
    "ax[0].scatter(np.asarray(class0)[:,0],\n",
    "              np.asarray(class0)[:,1],marker=\"*\",color=\"r\",s=3,label=\"class0\")\n",
    "ax[0].scatter(np.asarray(class1)[:,0],\n",
    "              np.asarray(class1)[:,1],marker=\"*\",color=\"orange\",s=3,label=\"class0\")\n",
    "ax[0].scatter(np.asarray(class2)[:,0],\n",
    "              np.asarray(class2)[:,1],marker=\"*\",color=\"purple\",s=3,label=\"class0\")\n",
    "ax[0].legend(loc=\"upper right\")\n",
    "ax[0].set_ylim([2.0,4.5])\n",
    "ax[0].set_xlim([4.0,8.0])\n",
    "\n",
    "class0_pred = []\n",
    "class1_pred = []\n",
    "class2_pred = []\n",
    "for idx,cls in enumerate(y_pred):\n",
    "    if cls == 0:\n",
    "        class0_pred.append(x_test[idx,:])\n",
    "    elif cls == 1:\n",
    "        class1_pred.append(x_test[idx,:])\n",
    "    else:\n",
    "        class2_pred.append(x_test[idx,:])\n",
    "ax[1].set_title(\"original test dataset class\")\n",
    "ax[1].scatter(np.asarray(class0_pred)[:,0],\n",
    "              np.asarray(class0_pred)[:,1],marker=\"*\",color=\"r\",s=3,label=\"class0\")\n",
    "ax[1].scatter(np.asarray(class1_pred)[:,0],\n",
    "              np.asarray(class1_pred)[:,1],marker=\"*\",color=\"orange\",s=3,label=\"class0\")\n",
    "ax[1].scatter(np.asarray(class2_pred)[:,0],\n",
    "              np.asarray(class2_pred)[:,1],marker=\"*\",color=\"purple\",s=3,label=\"class0\")\n",
    "ax[1].legend(loc=\"upper right\")\n",
    "ax[1].set_ylim([2.0,4.5])\n",
    "ax[1].set_xlim([4.0,8.0])\n",
    "\n",
    "class0_test = []\n",
    "class1_test = []\n",
    "class2_test = []\n",
    "for idx,cls in enumerate(y_test):\n",
    "    if cls == 0:\n",
    "        class0_test.append(x_test[idx,:])\n",
    "    elif cls == 1:\n",
    "        class1_test.append(x_test[idx,:])\n",
    "    else:\n",
    "        class2_test.append(x_test[idx,:])\n",
    "ax[2].set_title(\"predict test dataset class\")\n",
    "ax[2].scatter(np.asarray(class0_test)[:,0],\n",
    "              np.asarray(class0_test)[:,1],marker=\"*\",color=\"r\",s=3,label=\"class0\")\n",
    "ax[2].scatter(np.asarray(class1_test)[:,0],\n",
    "              np.asarray(class1_test)[:,1],marker=\"*\",color=\"orange\",s=3,label=\"class0\")\n",
    "ax[2].scatter(np.asarray(class2_test)[:,0],\n",
    "              np.asarray(class2_test)[:,1],marker=\"*\",color=\"purple\",s=3,label=\"class0\")\n",
    "ax[2].legend(loc=\"upper right\")\n",
    "ax[2].set_ylim([2.0,4.5])\n",
    "ax[2].set_xlim([4.0,8.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "10f1fb42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7666666666666667"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy = accuracy_score(y_pred, y_test)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f840ab6",
   "metadata": {},
   "source": [
    "# 降维处理\n",
    "## 维数灾难 curse of dimensionality\n",
    "经过极差对所有维度进行标准化变换后，我们可以将n个样本点视为p维单位超立方体中均匀分布的n个点<br>\n",
    "Bellman研究表明，假设样本点$X_0$处于超立方体的一个顶点位置，找到他的近邻比率$r$（近邻数量占全部数据量的比值）时超立方体各边的期望边界长度为\n",
    "$$\n",
    "    Ed_p(r) = r^{\\frac{1}{p}}\n",
    "$$\n",
    "也就是说，对于一个$p=10$的10维空间而言，要找到$r=0.01$或者$r=0.1$的近邻，$Ed(0.01)=0.01^{\\frac{1}{10}}=0.63$和$Ed(0.1)=0.1^{\\frac{1}{10}}=0.8$，计算结果表明取值距离跨越了总长度的$63\\%$和$80\\%$<br>\n",
    "与此同时，单纯减少r的量值也不能够对超立方体各边界期望长度的减少做出多大贡献，但是同时会增大预测的方差<br>\n",
    "以上推导从一个侧面证明当维度增高时，数据点在高维度空间中的分布将不再平均，它们将更多集中在空间的边缘位置，从而导致算法的开销明显增大<br>\n",
    "下面我们将介绍两种降维的思路，其一是基于线性变化的思想，另一种则是利用低维嵌入的思想"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "966183f2",
   "metadata": {},
   "source": [
    "## 线性变换 Linear Transformation\n",
    "一般来说，最简单的维度变换即为对原始高维空间进行线性变换，给定d维空间中的样本\n",
    "$$\n",
    "    \\mathbf{X}=\\{\\mathbf{x_1},\\mathbf{x_1},\\cdots,\\mathbf{x_m}\\}\n",
    "$$\n",
    "变换后得到$d^{\\prime}<d$维空间中的样本\n",
    "$$\n",
    "    Z = W^TX\n",
    "$$\n",
    "其中$W\\in \\mathbb{R}^{d\\times d^\\prime}$是变换矩阵，$Z\\in \\mathbb{R}^{d^\\prime \\times m}$是样本在新空间中的表达<br>\n",
    "接下来，我们根据变换后对于低维子空间性质的不同要求可以构造出相应的最优化问题，并对$W$施加不同约束，<br>\n",
    "最常见的线性变换包括LDA以及PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4b2a3ee",
   "metadata": {},
   "source": [
    "### LDA - 线性判别分析\n",
    "传统的LDA是二分类线性判别模型，属于有监督学习的范畴，放在这里是因为我们的确使用到了线性变换的模型思路<br>\n",
    "与此同时，我们可以通过OVO或是OVR的组合模式将该二分类模型扩展至多分类模型之中<br>\n",
    "在该线性变换模型中，我们将对高维空间($n$维)中的数据点投影到$n-1$维度的超平面上，投影后的点将按照类别进行区分<br>\n",
    "相应的约束条件是：投影后类内方差最小，类间方差最大<br>"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "812899dc",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)\n",
    "LDA二维示意图【实际上可能有多维】，其中“+”和“-”分别代表正例和反例"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1617c96",
   "metadata": {},
   "source": [
    "首先，我们定义数据集中的主要变量<br>\n",
    "给定数据集\n",
    "$$D=\\{(x_i,y_i)\\}^{m}_{i=1}, y_i \\in (0,1)$$\n",
    "令$X_i,\\mu_i,\\Sigma_i$分别为第$i \\in (0,1)$类实例的集合、均值向量和协方差矩阵<br>\n",
    "若将数据投影到直线$\\mathbf{\\omega}$上，我们可以分别得出两类样本均值和协方差矩阵的投影分别为\n",
    "$$\\mathbf{\\omega}^T\\mathbf{\\mu_0},\\mathbf{\\omega}^T\\mathbf{\\mu_1},\\mathbf{\\omega}^T\\mathbf{\\Sigma_0}\\mathbf{\\omega},\\mathbf{\\omega}^T\\mathbf{\\Sigma_1}\\mathbf{\\omega}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "110a5ccf",
   "metadata": {},
   "source": [
    "欲使得同类样本投影点尽可能接近，即同类样本投影点的协方差尽可能小，我们需要\n",
    "$$ \\mathbf{\\omega}^T\\mathbf{\\Sigma_0}\\mathbf{\\omega}+ \\mathbf{\\omega}^T\\mathbf{\\Sigma_1}\\mathbf{\\omega}$$\n",
    "尽可能小"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5754b39e",
   "metadata": {},
   "source": [
    "欲使得异类样本投影点尽可能远离，即类中心之间距离尽可能大，我们需要\n",
    "$$ ||\\mathbf{\\omega}^T\\mathbf{\\mu_0}-\\mathbf{\\omega}^T\\mathbf{\\mu_1}||^{2}_{2}$$\n",
    "尽可能大"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b13892f2",
   "metadata": {},
   "source": [
    "同时考虑二者，我们可以通过比率的方法构造最优化问题的目标函数\n",
    "$$ \n",
    "\\begin{array}{ll}\n",
    "J & = & \\frac{||\\mathbf{\\omega}^T\\mathbf{\\mu_0}-\\mathbf{\\omega}^T\\mathbf{\\mu_1}||^{2}_{2}}{\\mathbf{\\omega}^T\\mathbf{\\Sigma_0}\\mathbf{\\omega}+ \\mathbf{\\omega}^T\\mathbf{\\Sigma_1}\\mathbf{\\omega}} \\\\\n",
    "& = &\\frac{\\mathbf{\\omega}^T(\\mathbf{\\mu_0}-\\mathbf{\\mu_1}){(\\mathbf{\\mu_0}-\\mathbf{\\mu_1})}^T\\mathbf{\\omega}}{\\mathbf{\\omega}^T(\\mathbf{\\Sigma_0}+\\mathbf{\\Sigma_1})\\mathbf{\\omega}}\n",
    "\\end{array}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52af1494",
   "metadata": {},
   "source": [
    "为了简化公式的书写，我们构造类内散度矩阵\n",
    "$$ S_w = \\mathbf{\\Sigma_0}+\\mathbf{\\Sigma_1}$$\n",
    "以及类间散度矩阵\n",
    "$$ S_b = (\\mathbf{\\mu_0}-\\mathbf{\\mu_1}){(\\mathbf{\\mu_0}-\\mathbf{\\mu_1})}^T$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad97e16b",
   "metadata": {},
   "source": [
    "则最优化问题目标函数可以重写为\n",
    "$$\n",
    "    J= \\frac{\\mathbf{\\omega}^TS_b\\mathbf{\\omega}}{\\mathbf{\\omega}^TS_w\\mathbf{\\omega}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94ac4cb7",
   "metadata": {},
   "source": [
    "由于最优化问题目标函数都是$\\mathbf{\\omega}$的二次项，这表明该问题与其长度无关<br>\n",
    "不失一般性，我们令分母$\\mathbf{\\omega}^TS_w\\mathbf{\\omega}=1$，则最优化问题可以表述如下：\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "    & \\mathop{\\arg\\min}_{\\omega} & -\\mathbf{\\omega}^TS_b\\mathbf{\\omega} \\\\\n",
    "    & s.t. & \\mathbf{\\omega}^TS_w\\mathbf{\\omega}=1\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e13ec41",
   "metadata": {},
   "source": [
    "求解该类最优化问题我们将使用拉格朗日乘子法配合KKT条件，这里不再赘述，最后得到分类直线方程为：\n",
    "$$\n",
    "    \\mathbf{\\omega} = {S_{\\omega}}^{-1}(\\mathbf{\\mu_0}-\\mathbf{\\mu_1})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7193d3a0",
   "metadata": {},
   "source": [
    "### LDA python 实现\n",
    "python sklearn 包中 LinearDiscriminantAnalysis 提供LDA功能"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e35ddef7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd \n",
    "import warnings \n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "iris_x, iris_y = load_iris(return_X_y=True)\n",
    "iris_x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "732902f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 2)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 注意，由于受到svd影响，输出降维后的矩阵实际上是（属性值-1）和（类别值-1）二者之间的最小值\n",
    "lda_model = LinearDiscriminantAnalysis(solver='svd')\n",
    "lda_model.fit(iris_x,iris_y)\n",
    "iris_transformed = lda_model.transform(iris_x)\n",
    "iris_transformed.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08085aa5",
   "metadata": {},
   "source": [
    "### PCA - 主成分分析\n",
    "主成分分析所要达到的主要目的在于能够使用一个低维的超平面更恰当的表达在高维中存在的各数据点<br>\n",
    "如何评价这样的超平面呢？我们有以下两种方式：\n",
    "1. 最近重构性： 样本点到这个超平面的距离足够近\n",
    "2. 最大可分性： 样本点在这个超平面上的投影能尽可能分开\n",
    "\n",
    "有趣的是，基于以上两种判别标准，我们能够分别推导出PCA相同的最优化问题"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c750a05",
   "metadata": {},
   "source": [
    "### PCA最近重构性\n",
    "假定样本进行了中心化，即\n",
    "$$\n",
    "    \\sum_{i}x_i = 0\n",
    "$$\n",
    "同时假定投影变换后得到的新坐标系为：\n",
    "$$\n",
    "    \\{\\omega_1,\\omega_1,\\cdots,\\omega_d\\}\n",
    "$$\n",
    "其中$\\omega_i$是标准正交基向量，这意味着\n",
    "$$\n",
    "\\left \\{\n",
    "\\begin{array}{ll}\n",
    "||\\omega_i||_2 = 1 \\\\\n",
    "{\\omega_i}^T{\\omega_j} = 0, (i \\ne j)\n",
    "\\end{array}\n",
    "\\right .\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d17eb3ca",
   "metadata": {},
   "source": [
    "PCA的目标是将维度降低到$d^{\\prime}<d$，那么样本点$x_i$在低位坐标系中的投影为\n",
    "$$z_i=(z_{i1},z_{i2},\\cdots,z_{id^\\prime})$$\n",
    "其中$z_{ij}={\\omega_j}^Tx_i$是$x_i$在低维坐标系下第j维的坐标<br>\n",
    "若基于$z_i$来重构$x_i$，则会得到\n",
    "$$ \\hat x_i = \\sum^{d^\\prime}_{j=1}z_{ij}\\omega_j$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec140790",
   "metadata": {},
   "source": [
    "那么，我们可以构造原样本点$x_i$与基于地位样本点重构的样本点$\\hat x_i$之间的距离\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "\\displaystyle\\sum_{i=1}^{m}\\lvert\\lvert\\displaystyle\\sum_{j=1}^{d^\\prime}z_{ij}\\omega_j-x_i||^2_2\n",
    "& = & \\displaystyle\\sum_{i=1}^{m}{z_i}^Tz_i - 2 \\displaystyle\\sum_{i=1}^{m}{z_i}^TW^Tx_i + const \\\\\n",
    "& \\propto & -tr(W^T\\displaystyle\\sum_{i=1}^{m}{z_i}^Tx_i) \\\\\n",
    "& \\propto & -tr(W^T\\displaystyle\\sum_{i=1}^{m}(W^Tx_i)^Tx_i) \\\\\n",
    "& \\propto & -tr(W^T(\\displaystyle\\sum_{i=1}^{m}x_i{x_i}^T)W)\n",
    "\\end{array} \n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96eef723",
   "metadata": {},
   "source": [
    "其中，$W$是一个$(d,d^\\prime)$变换矩阵，根据最近重构性、也就是重构前后样本点距离相差最小原则，以上距离应当被构造成最优化问题中的最小化结构，<br>考虑到$\\omega_i$是标准正交基，$\\displaystyle\\sum_{i=1}^{m}x_i{x_i}^T$是协方差矩阵，因此我们构造最优化问题如下：\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "    \\mathop{\\arg\\min}\\limits_{W} & -tr(W^TX{X}^TW) \\\\\n",
    "    s.t. & W^TW = I \\\\\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f287e13d",
   "metadata": {},
   "source": [
    "### PCA最大可分性"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cd314e5",
   "metadata": {},
   "source": [
    "从最大可分性出发，我们知道，投影后的样本点可以表示为$W^Tx_i$,<br>若要求所有样本点在投影后能够尽可能分开，就要求投影后样本点之间的方差最大<br>投影哦呼样本点之间的方差为$\\sum_i W^Tx_i{x_i}^TW$,于是我们可以构造相应的优化问题如下：\n",
    "$$\n",
    "\\begin{array}{ll}\n",
    "    \\mathop{\\arg\\max}\\limits_{W} & tr(W^TX{X}^TW) \\\\\n",
    "    s.t. & W^TW = I \\\\\n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52f42cd5",
   "metadata": {},
   "source": [
    "### PCA求解及说明"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a9582a1",
   "metadata": {},
   "source": [
    "我们可以发现，两种方法得到的最优化问题是对偶的。<br>\n",
    "使用拉格朗日乘子法求解最优化问题，可得：\n",
    "$$\n",
    "    XX^T\\omega_i = \\lambda_i\\omega_i\n",
    "$$\n",
    "接下来我们对$XX^T$进行特征值分解，讲求的的特征值排序，取前$d^\\prime$个特征值对应的特征向量构成$W^*$，该矩阵即为线性变换矩阵"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c109714",
   "metadata": {},
   "source": [
    "但是我们需要注意的是，PCA模型的解释性是较低的，从另一种角度来说即为PCA降维后得到的特征是偏离原特征的实际价值的，我么只能从数学角度认为PCA处理后的特征能够更清晰地区分不同类别，但是不能够说明新生成的特征具备具体的物理意义。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "627c9809",
   "metadata": {},
   "source": [
    "### PCA python实现\n",
    "python sklearn decomposition.PCA 包提供PCA的相关操作<br>\n",
    "需要注意的是，PCA包中实际使用的是svd替代方阵的特征值分解，这样做的目的是减少计算开销并且尽可能小的影响精度"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40044213",
   "metadata": {},
   "source": [
    "现在我们对sklearn.decomposition.PCA的主要参数做一个介绍：\n",
    "> 1. n_components：这个参数可以帮我们指定希望PCA降维后的特征维度数目。最常用的做法是直接指定降维到的维度数目，此时n_components是一个大于等于1的整数。当然，我们也可以指定主成分的方差和所占的最小比例阈值，让PCA类自己去根据样本特征方差来决定降维到的维度数，此时n_components是一个（0，1]之间的数。当然，我们还可以将参数设置为\"mle\", 此时PCA类会用MLE算法根据特征的方差分布情况自己去选择一定数量的主成分特征来降维。我们也可以用默认值，即不输入n_components，此时n_components=min(样本数，特征数)。\n",
    "> 2. whiten：判断是否进行白化。所谓白化，就是对降维后的数据的每个特征进行归一化，让方差都为1.对于PCA降维本身来说，一般不需要白化。如果你PCA降维后有后续的数据处理动作，可以考虑白化。默认值是False，即不进行白化。\n",
    "> 3. svd_solver：即指定奇异值分解SVD的方法，由于特征分解是奇异值分解SVD的一个特例，一般的PCA库都是基于SVD实现的。有4个可以选择的值：{‘auto’, ‘full’, ‘arpack’, ‘randomized’}。randomized一般适用于数据量大，数据维度多同时主成分数目比例又较低的PCA降维，它使用了一些加快SVD的随机算法。 full则是传统意义上的SVD，使用了scipy库对应的实现。arpack和randomized的适用场景类似，区别是randomized使用的是scikit-learn自己的SVD实现，而arpack直接使用了scipy库的sparse SVD实现。默认是auto，即PCA类会自己去在前面讲到的三种算法里面去权衡，选择一个合适的SVD算法来降维。一般来说，使用默认值就够了。\n",
    "\n",
    "除了这些输入参数外，有两个PCA类的成员值得关注。第一个是explained_variance_，它代表降维后的各主成分的方差值。方差值越大，则说明越是重要的主成分。第二个是explained_variance_ratio_，它代表降维后的各主成分的方差值占总方差值的比例，这个比例越大，则越是重要的主成分"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "213536b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd \n",
    "import warnings\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "iris_x, iris_y = load_iris(return_X_y=True)\n",
    "iris_x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "12304870",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=2)\n",
    "iris_de = pca.fit_transform(iris_x)\n",
    "iris_de.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63b60867",
   "metadata": {},
   "source": [
    "## 多维缩放 Multiple Dimensional Scaling\n",
    "多维缩放是另一种降维处理的思路，我们强调缩放前后向量的某种特性保持不变，<br>\n",
    "这种认识可以理解为我们只关心高维空间中某一个低维的分布，就好像这个低维分布是这个高维分布中的一个嵌入<br>\n",
    "因此，MDS追求原始空间中样本之间的距离在低维空间中得以保存"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acf7ec5d",
   "metadata": {},
   "source": [
    "## R代码实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2068ebe5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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